As someone pointed out in some thread a ways back, nuclear naval vessels like subs and carriers work because an oceanful of cold water is an excellent heat sink providing temperature differential.
What if we, instead, employ the sub-zero arctic/antarctic air to cool our atomic pile?
A ground-speed counterpart to Project Pluto/SLAM?
The snow cruiser is one of my favorite things. I didn’t see the most recent photos of it in the posted links. It was spotted buried but partially exposed on the edge of an iceberg (possibly). Presumably at the bottom of the ocean by now.
I doubt the committees would approve of nuclear power. People are extremely careful about introducing anything to the Antarctic. You can’t even bring in live plants to eat unless they are such that the cold would kill them completely if they got loose. No seeds, no research animals, no medical experiments etc.
Antarctic air still has about 70–80% of the thermal energy that “room temperature air” has; in Kelvin, we’re talking about the difference between 290 K and 230 K, or something along those lines. So if air-cooled nuclear reactors aren’t feasible in temperate climates, I’m skeptical that they would be feasible in Antarctica.
As well, land vehicles are much more sensitive to weight than are water vehicles. The delta-T problem you cite, plus the low thermal conductivity of air vs water implies the radiators are huge. Huge = heavy. Heavy = bad.
The need to rad-shield a reactor in a fairly small, confined space is also real unhelpful.
Don’t forget the specific heat of air vs. that of water. Changing the temperature of a volume of water takes a lot of energy, but changing the temp of the same volume of air takes roughly 1/4 as much.
So you have to heat up four times as much air by volume as you would water. So since you don’t have that much heating room to begin with, like @MikeS points out, and you’re having to use four times the volume, it’s probably not feasible.
You might, however, be able to scoop up a big bunch of snow every so often, and dump it when it gets too hot. That way, you’d still get the specific heat of water, as well as the heat of fusion.
It’s been done before, though. McMurdo hosted a nuclear reactor for a decade. Unfortunately, it did have some safety issues and so it was decommissioned.
The Antarctic Treaty does prohibit nuclear weapons testing and the disposal of nuclear waste on the Antarctic continent. But as noted by Dr. Strangelove above (irony!), actual nuclear reactors are not prohibited.